Internal Friction and Nonequilibrium Unfolding of Polymeric Globules

The stretching response of a single collapsed homopolymer is studied using Brownian dynamic simulations. The irreversibly dissipated work is found to be dominated by internal friction effects below the collapse temperature, and the internal viscosity grows exponentially with the effective cohesive strength between monomers. These results explain friction effects of globular DNA and are relevant for dissipation at intermediate stages of protein folding.

Figure 1

Top: Snapshots of a relax-stretch cycle for a polymer with $N=100$ monomers and cohesive strength $\widetilde{ϵ}=ϵ/k_{B}T=2.08$. The stills are taken at equally spaced times and span a whole cycle; i.e., the first and the final snapshots correspond to fully elongated configurations. Bottom: Force-extension traces for $\widetilde{ϵ}=2.08$ and 4.1. The blue and red curves correspond to relaxation and stretching, respectively, as indicated in the lowest panel. The stretching velocity in all plots is set to $\tilde{v}=v\tau /a=0.0045$.

Figure 2

(a) Averaged stretching curves for $N=50$ and different cohesive strengths $\widetilde{ϵ}=0$, 1.25, 2.08, 2.91, and 4.1 (from bottom to top) at $\tilde{v}=0.0045$. The dashed lines indicate the fitted plateau force $F_p$. (b) $F_p$ as a function of $\widetilde{ϵ}$ for two different chain lengths. The lines are linear fits to the data (see text for details).

Figure 3

(a) Stretching traces for $N=100$ and $\widetilde{ϵ}=2.08$ at different pulling velocities $\tilde{v}=0.1125$, 0.09, 0.045, 0.0225, and 0.0045 (from top to bottom). Inset: The dissipated work $\Delta W$ is defined as the area between the top trace (here $\tilde{v}=0.09$) and the one for $\tilde{v}=0.0045$. (b) Dissipated work per monomer $\Delta W/(N{k}_{B}T)$ as a function of the rescaled velocity $\tilde{v}N$ for different cohesive strengths $\widetilde{ϵ}$ and $N$. Linear fits according to Eq. (2) with $\gamma =1$ yield the internal viscosity ${\eta }_G$.

Figure 4

Rescaled dissipated work, equivalent to the excess internal viscosity $\Delta W/\Delta W_0-1\simeq {\eta }_G/{\eta }_0-1$, obtained from the linear fits in Fig. 3b as a function of the effective cohesive strength $\widetilde{ϵ}-{\widetilde{ϵ}}_c$. The broken line denotes Eq. (3) with $\theta =1.125$ and the solid lines the confidence interval due to the error in ${\widetilde{ϵ}}_c$.